1/2x+6x-2=20

Solution for 1/2x+6x-2=20 equation:

1/2x+6x-2=20

We move all terms to the left:

1/2x+6x-2-(20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6x+1/2x-22=0

We multiply all the terms by the denominator


6x*2x-22*2x+1=0

Wy multiply elements

12x^2-44x+1=0

a = 12; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·12·1
Δ = 1888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{118}}{2*12}=\frac{44-4\sqrt{118}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{118}}{2*12}=\frac{44+4\sqrt{118}}{24}
$